7. An urn contains 4 red balls and 8
white balls. 2 balls are drawn at random. Use a tree diagram to
construct a probabilistic model for this experiment. Use the model to
answer the following questions.

a) What is the probability of having at least 1 white ball?

b) What is the probability that the balls are the same color?

c) What is the probability that the second ball is white?

d) What is the probability that the second ball is white given
that the balls are the same color?

e) Are the events in b) and c) independent?

f) What is the expected number of white balls?

8. An instructor passed out midterm
reports after the first test. The report contained a homework grade
and a test grade. 30% of the class got unsatisfactory grades on both
the homework and the test. 60% got satisfactory grades on the
homework, and 50% got satisfactory grades on the test.

a) What percent of the class got satisfactory grades on both
the test and the homework?

b) What percent of the students who got satisfactory grades on
the homework got satisfactory grades on the test?

c) Are getting satisfactory grades on the test and the
homework independent events?

9. Linda took a multiple choice test. Each questionhad 4 possible answers from which to choose.There were 6 questions where she had to guess. Make up a probability distribution for this exeriment.